Harvesting of Bending Waves in One-Dimensional Infinite Beams Using Resistive-Reactive Circuits

Vibration-to-electricity conversion has been heavily researched over the last decade with the ultimate goal of enabling self-powered small electronic components to use in wireless applications ranging from medical implants to structural health monitoring sensors. Regardless of the transduction mechanism used in transforming vibrational energy into electricity, the existing research efforts have mostly focused on deterministic or stochastic harvesting of direct vibrational energy available at a fixed location in space. Such an approach is convenient to design and employ linear and nonlinear vibration-based energy harvesters, such as base-excited cantilevers with piezoelectric laminates. Although the harvesting of local vibrations using linear and nonlinear devices has been well studied, there has been little effort to investigate power extraction from elastic waves propagating in host structures to gain a fundamental understanding of power flow and to best exploit not only standing but also traveling wave energy. This paper explores the problem of piezoelectric energy harvesting from one-dimensional bending waves involving propagating and evanescent components with a focus on infinitely long thin beams. A pair of electroded piezoelectric patches is implemented as the energy harvesting interface connected to a complex electrical load. An analytical modeling framework is given in order to relate the harvested power to incoming wave in the presence of a generalized resistive-reactive circuit. Effects of energy harvesting on the global wave dynamics as well as individual propagating and evanescent wave components are investigated with an emphasis on the wavelength matching concept. The electrical loading conditions for maximum power and efficiency are identified for several special cases in the low frequency range.